Question

A study looked at if TV show content influenced the ability of watchers to remember brand names of items in commercials. Researchers randomly assigned volunteers to watch one of three programs, each containing the same nine commercials. After the show ended, the volunteers were asked to remember the brands of products that were advertised. Below shows how many of the nine commercials the volunteers remembered correctly:

Program | Size | Mean | SD

Violent | 108 | 2.08 | 1.87

Sexual | 108 | 1.71 | 1.76

Neutral | 108 | 3.17 | 1.77

1. Perform an hypothesis test. State the hypotheses, t-stat, p-value, and conclusion.

2. Using a Bonferroni adjustment, find simultaneous 95% confidence intervals for the pairwise differences in means, and refine your conclusion from part (1). (so a set of 3 confidence intervals.)

Answer 1

One Way Analysis of Variance (ANOVA)              

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance	std dev
A	108	224.64	2.080	3.497	1.8700
B	108	184.68	1.710	3.098	1.7600
C	108	342.36	3.170	3.133	1.7700
					#VALUE!
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	124.438	2	62.219	19.189	0.0000	3.02
Within Groups	1040.832	321	3.242
Total	1165.269	323

Bonferroni adjustment

α=0.05/3 = 0.0167

Level of significance=	0.0167
no. of treatments,k=	3
DF error =N-k=	321
MSE=	3.2425
t-critical value,t(α/2,df)=	2.4066

			confidence interval
population mean difference	critical value	lower limit	upper limit	result	test stat	p value
µ1-µ2	0.370	0.58972	-0.2197	0.9597	means are not different	1.510	0.1320
µ1-µ3	-1.090	0.59	-1.68	-0.50	means are different	-4.448	0.0000
µ2-µ3	-1.460	0.59	-2.05	-0.87	means are different	-5.958	0.0000